Quantum valley Hall effect, orbital magnetism, and anomalous Hall effect in twisted multilayer graphene systems

Understand

We study the electronic structures and topological properties of $(M+N)$-layer twisted graphene systems.

• We consider the generic situation that $N$-layer graphene is placed on top of the other $M$-layer graphene, and is twisted with respect to each other by an angle $\theta$.
• In such twisted multilayer graphene (TMG) systems, we find that there exists two low-energy flat bands for each valley emerging from the interface between the $M$ layers and the $N$ layers.
• These two low-energy bands in the TMG system possess valley Chern numbers that are dependent on both the number of layers and the stacking chiralities.